Diketahui a=i+j, b=2i-3j+k, dan c=4j+3k, carilah :a. b x a

a. -i + j + 5k, b. -13i - 6j + 8k, c. 8i - 8j + 7k

Pembahasan

Untuk menyelesaikan soal ini, kita perlu melakukan operasi perkalian silang (cross product) pada vektor-vektor yang diberikan.

a. b x a
b = 2i - 3j + k
a = i + j

b x a = 
| i   j   k  |
| 2  -3   1  |
| 1   1   0  |

= i((-3)(0) - (1)(1)) - j((2)(0) - (1)(1)) + k((2)(1) - (-3)(1))
= i(0 - 1) - j(0 - 1) + k(2 + 3)
= -i + j + 5k

b. b x c
b = 2i - 3j + k
c = 4j + 3k

b x c = 
| i   j   k  |
| 2  -3   1  |
| 0   4   3  |

= i((-3)(3) - (1)(4)) - j((2)(3) - (1)(0)) + k((2)(4) - (-3)(0))
= i(-9 - 4) - j(6 - 0) + k(8 - 0)
= -13i - 6j + 8k

c. a x (b x c)
a = i + j
b x c = -13i - 6j + 8k

a x (b x c) = 
| i   j   k  |
| 1   1   0  |
| -13 -6   8  |

= i((1)(8) - (0)(-6)) - j((1)(8) - (0)(-13)) + k((1)(-6) - (1)(-13))
= i(8 - 0) - j(8 - 0) + k(-6 + 13)
= 8i - 8j + 7k